Methods for calculating errors of a function whose arguments have individual errors.

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Gini index on data with error margins

I have data series and I want to calculate Gini coefficients for each row as an estimate of matrix sparsity. Hoever values contained in the rows are not exact and have error bounds. My question is ...
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9 views

Error propagation and Standard Deviation

I never quite got the hang of this during my entry stat course and it has been bugging me for a long time now. Lets assume I'm trying to find the focal length of a concave lens. Using a mockup ...
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24 views

Propagation of uncertainty (intersection of two graphs)

The situation is as follows: I performed necessary measurements and used them to create two graphs. I used polynomial regression to find the point of intersection. What I know: precision of ...
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24 views

Trying to impelement IRPROP+

I'm stuck I tried 3 times to setup IPROP+. I figured IPROP+ was the most highly rated of the three found here http://heatonresearch.com/wiki/RPROP Problem is... my training doesn't seem to work. ...
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49 views

Entropy, Softmax and the derivative term in Backpropagation

I'm currently interested in using Cross Entropy Error when performing the BackPropagation algorithm for classification, where I use the Softmax Activation Function in my output layer. From what I ...
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26 views

Propogation of error in a matrix inversion

I'm trying to find the deterministic error bounds for some parameters calculated through distance geometry. The equation can be simplified to the following form: $ \left[\begin{matrix} x_1 \\ x_2 \\ ...
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1answer
21 views

The probability of m out of K things being wrong with an error of ɛ

I have a homework question about a machine-learning algorithm that uses ensemble learning with simple majority voting. Assuming we have K hypotheses, each with an error ɛ, the question asks us to ...
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1answer
39 views

What does correlation mean in error propagation?

From the python uncertainties package: Correlations between expressions are correctly taken into account. Thus, x-x is exactly zero, for instance (most implementations found on the web yield a ...
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29 views

Error propagation - nonnormal (again)

I have a dataset of ~2000 points. Each of those points has a standard error value associated with it, and it is assumed that the data points and errors are uncorrelated. Both the dataset and the ...
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19 views

Error propagation through convolution

I have a list of data points $y_i$ and a respective uncertainty $\sigma_i$ associated to them. Now I am convoluting this with a Gaussian window function (discretized $w_i$) "numpy.convolve" function ...
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19 views

Error propagation with the bootstrap method

I am trying to estimate the value of a function (essentially a standard deviation) from a series of experimental data. The value, v, is broadly given by $$ v = \sigma(F(\textbf{x}),F(\textbf{y}), ...
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49 views

propagation of standard error in a sum of proportions

I am new to error propagation, and I am trying to solve a simple problem: I am trying to calculate the estimate and standard error of a parameter (carbon density) across a landscape composed of ...
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32 views

propagation of the error in the summation

I have a question regarding the propagation of the error during the summation. Please see the equation below. In this equation only quantity R has an error. How it will propagate to the final value ...
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30 views

Error propagation and p value

Say I have parameters $a(x$) and $b(x)$, with $N_a(x)$ and $N_b(x)$ experimental measurement counts, respectively. $x$ is an independent variable ($x_1, x_2, ...$). For each $a$ and $b$, I can ...
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20 views

Error in standard deviation and variance from error in data

I have a set of datapoints $x_i$ which have known upper bounds for absolute errors $\delta x_i$. (To clarify, this means each $x_i$ is actually $x_{i_0} \pm \delta x_i$). For simplicity, assume that ...
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36 views

time-series forecasting - predicting av. error intervals

I should start with the disclaimer I'm not proficient with R or heavier statistical terminology, sadly! Nevertheless I create sales forecasts (using different methods such as holt-winters), and I'm ...
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18 views

Tools for determining final error with mixture of correlated and independent sources of error

Preface: Not looking for an answer, but rather seeking an approach or set of approaches to deal with a complicated problem. Brief version: I have a single, analytical set of 3 equations with 8 ...
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22 views

How to properly consider uncertainty propagation in random variables

I have 34 input random variables and one output random variable, named R. From 33 input random variables and some dataset I determined the best predictive ...
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16 views

Error estimation in peak location determination by centroid method

I am trying to locate peak in a data set by numerically calculating the peak using centroid method. How can I estimate the error associated with this peak determination?
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2answers
250 views

Background subtraction for signal and error analysis

I use a CCD to see the split of a energy level due to Zeeman effect. I have a 1 dimensional CCD of 7926 pixel of 7μm each one. My CCD analyze a region 2 dimensional, and then it steps forward 200 ...
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139 views

Error for combining multiple binomial distributions

This problem is somewhat involved and I have a partial solution so bear with me. I will illustrate the problem with an example. Lets say we have two processes and we want to know which has a higher ...
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77 views

Propagation of Poisson Confidence Intervals

I have a set of measurement with 95% Poisson confidence intervals, and I would like to subtract and multiply them and propagate the error. For example, I measured the copy number of a piece of DNA in ...
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973 views

Standard deviation of normalized data

I have a data set $y_i$ (where the $y_i$ are photon counts in time period $i$, $i=1,2,...,n$, assumed Poisson), with an estimated standard error $s_i$ (= $\sqrt{y_i}$) for each count. For some ...
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41 views

Error Propagation Calculation

I have a few machines that are used to calibrate each other. Machine 1 has is accurate to 0.025% Machine 1 is used to calibrate Machine 2, which has an accuracy of 0.005% Machine 2 is used to ...
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How do I propagate error when X+Y=1 and aX+bY=1?

I have data for proportions of two diet categories X and Y (from gut samples, n=10) that must sum to 1. I am multiplying each by a different constant (a and b) and then re-calculating the two ...
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2answers
82 views

Statistical error and error propagation

I have a quantity defined as: $P_{frac} = \frac{F_{max}-F_{min}}{F_{max}+F_{min}}$ I also have the value for $F_{max}$, $F_{min}$, and their statistical errors. How can I calculate the error for ...
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151 views

Error propagation calculation yielding negative variance

I am trying to calculate the standard deviation of the sum X = A + B. A and B are mean values, and I do not have access to the source data. A is 0.46 with an SD of 0.014 (SDa) and B is 0.375 with an ...
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132 views

How to compare two groups of empirical distributions?

I am working with EEG and now I am trying to compare coherence for two groups of individuals. Problem is coherence is dependent on length of signal but I have signals with different length for each ...
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1answer
66 views

Reusing predicted values as independent variables for new linear regression

Edit I've rephrased this question severely. Suppose I have a fitness center, and instead of a monthly fee, the people are paying for courses they are taking. I've got the monthly total revenue of all ...
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1answer
189 views

Weighted average of measurements with unequal errors

Suppose I have the numbers below. Consider them as results of some measurement. ...
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50 views

Regression with error in covariates

I am looking for some advice for a colleague who is dealing with regression models for which it is know, that the continuous covariate of interest $X_1$ was measured with error. More precisely, we ...
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1answer
116 views

Possible Paradox: Calculating a confidence interval with within-experiment error

This is a spinoff of How to calculate the confidence interval of the mean of means? and related to When making inferences about group means, are credible Intervals sensitive to within-subject ...
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1answer
472 views

When making inferences about group means, are credible Intervals sensitive to within-subject variance while confidence intervals are not?

This is a spin off of this question: How to compare two groups with multiple measurements for each individual with R? In the answers there (if I understood correctly) I learned that within-subject ...
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3answers
2k views

How to compare two groups with multiple measurements for each individual with R?

I have a problem like the following: 1) There are six measurements for each individual with large within-subject variance 2) There are two groups (Treatment and Control) 3) Each group consists of ...
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388 views

Average over two variables: Why do standard error of mean and error propagation differ and what does that mean?

I'm doing an experiment with a cryostat to determine the critical temperature for lead. To avoid asymmetries, I determine the critical temperature both through heating (going from 2 K to 10 K) and ...
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1k views

Multiplication and division of values with geometric standard deviation

What is the geometric standard deviation of a value, which is the result of dividing two independent values, each of which has its own geometric standard deviation ? It is a frequent situation in ...
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276 views

Division of two poisson variables

Let's say I have four variables $x_1, x_2, x_3$ and $x_4$ all distributed as Poisson, with means $\lambda_i$, and standard deviations respectively. Now I want to calculate two further variables $y_1= ...
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158 views

Error of the sum of complex numbers

I'm analyzing the effect of precision error in optics experiments. One of the relevant quantities is a sum of $N$ complex numbers, each with a complex relative standard error $\epsilon$. How can I ...
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211 views

Formal errors from non-negative least-squares?

I have seen a couple of similar questions, but none with answers, so perhaps I can formulate this question in a way that will be answerable. I am computing a standard linear regression subject to a ...
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247 views

Error propagation SD vs SE

I have 3 to 5 measures of a trait per individual in two different conditions (A and B). I'm plotting the average for each individual in each condition and I use the standard error (i.e., ...
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41 views

Explaining the difference between error propagation and “grand variance”?

I have the following data concerned with simple radiation detection. I collect a background dose $B$ for 100 seconds and find the standard deviation and get the uncertainty $E_B$. I then take 10 ...
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89 views

Calculate effect of independent variable

If $a\times b\times c=t$ and I change $a$, $b$, and $c$, how do I calculate the effect of each change. I believe the equation is: $(a+\Delta a)(b+\Delta b)(c+\Delta c)=(t+\Delta t)$, and then I solve ...
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58 views

Combining errors

I've got this tricky problem to solve. Hope somebody can help me. Let's suppose I want to know the mean radius of the trees in a wood. For each tree i I measure the radius at the top, at tha center ...
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1answer
219 views

Simulating Monte Carlo with different standard deviations and interval confidence

I have a question regarding Monte Carlo simulation (direct simulation), applied to propagation of uncertainties. From what I understand Monte Carlo accepts random numbers of each input variable of ...
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41 views

posterior covariance for linear inversion

I am performing a physical experiment where the unavoidably inaccurate setup likely creates errors in the inversion of the data for the model. Let's assume a linear relationship between data $\mathbf ...
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625 views

Uncertainty propagation in linear interpolation

How do I calculate the uncertainties in linearly interpolated values from a given tabulated function? I am just coming back into the fold after a bit of a hiatus, and am having trouble ...
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1answer
43 views

Combining observed Gaussian error with common fractional model error

I'm currently trying to incorporate model errors into a likelihood function to fit the model to some results. Let's just call them $x_{m,i}$ for the model and $x_{o,i}$ for the $N$ observations, ...
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1answer
111 views

How do I calculate the error propagation of this function?

I'm using a molecular biological method which requires the following normalization $$Q = \frac{A}{\sqrt[k]{\prod_{i=1}^k B_i}}.$$ How can I find the standard deviation of $Q$, given that $A$ and ...
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404 views

Error propagation with linear regression

I'm trying to obtain an estimation of the uncertainty related to an analytical method: my function is just a linear regression $f: y=ax+b+ \epsilon$ with $y_i=\frac{R_i}{C}$, both $R$ and $C$ are ...
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1k views

Standard error of fold changes

I have a conceptual problem to understand the standard error of the ratio of two random variables after error propagation. Let $X$ and $Y$ be two random variables with means $\bar x$ and $\bar y$ and ...